451102 Surveying for Builders B'P'D'

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Maps and Plans Basic Computations Geometrical
Concepts Errors and Statistics
Background
Distances Angles Height differences
coordinates heights
Measurements
Mid Semester examination
New Technologies
GPS
Practical Surveying
Setting Out
Analysis
Geographical Information Systems
Legalities involved
Cadastral Surveying
Computer assisted surveying
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The Department of Geomatics451-102 Surveying
for Builders
Lecture 2 Maps and Plans in Surveying/Basic
Computations/Geometrical Concepts Allison Kealy
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Maps and Plans in Surveying..

• Surveys are carried out to make maps and plans.
• Maps and plans are used to carry out surveys.

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Survey Types

• Detail
• Control
• Setting Out
• Heighting

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Surveying Terminology

• Survey area
• Coordinates
• Control Points
• Datums
• North

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Elements of a map eg

• North - directions
• Grid
• Coordinates
• Scale - distances
• Heights

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What is involved in conducting a survey?

• What are the measurements made?
• What do these measurements mean?
• What further computations are required?
• How good are our measurements?

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What are the measurements made?

• angles (degs,mins,secs, rads)
• distances (m, km)
• Height differences (m)

1000m 1km 100cm 1m 10mm 1cm 1000mm 1m
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What do these measurements mean?

• Angles
• angles between points (eg)
• bearings

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Basic Computation 1 Converting degrees, minutes,
seconds to decimal degrees and radians
Angle measured 28o 31' 25" 1o 60' 1'
60" therefore 1o 3600" To convert to decimal
degrees 28 31/60 25/3600
28.5236o p
radians 180o where p 3.1416 To convert
decimal degrees to radians 28.5236 x p/180

0.497831rads
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Basic Computation 2 Converting radians to
decimal degrees, and degrees, minutes and seconds
To convert radians to decimal degrees 0.497831
x 180/p
28.5236o To convert
decimal degrees to degs, mins, secs degs
28 mins (28.5236 - 28 ) x 60 31.416 31 secs
(31.416 - 31) 60 24.96 25 28o 31' 25"
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North Directions and Whole Circle Bearings

• True, magnetic, arbitrary, grid

N
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Further Computations from the Measurements

• Compute the distance and direction between two
  points given their coordinates.
• Computing the coordinates of an unknown point
  given the coordinates of a known point and the
  direction and distance between them.

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Basic Computation 3 Computing the distance
between two points given their coordinates -
Chart 3.xls
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Basic Computation 4 Computing the bearing
between two points given their coordinates -
Chart 2 .xls
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Basic Computation 5 Computing the coordinates of
a point given the bearing and distance from a
known point Chart 4.xls
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Worked Example - Computation of Rectangular
Coordinates
The coordinates of a point A are 311.617m E,
447.245m N. Calculate the coordinates of point B
where qAB 37o 11 20 and sAB 57.916m.
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Worked Example - Computation of bearing and
distance
The coordinates of point A are 469.72m E, 338.46
N and point B are 268.14m E and 116.19mN.
Compute the bearing and distance between them.
180o
Problem with quadrants!
qAB 222o 12 19
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Inverse Calculations
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Maps and Plans Basic Computations Geometrical
Concepts Errors and Statistics
Background
Distances Angles Height differences
coordinates heights
Measurements
Mid Semester examination
New Technologies
GPS
Practical Surveying
Setting Out
Analysis
Geographical Information Systems
Legalities involved
Cadastral Surveying
Computer assisted surveying
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How good are our measurements?

• precision
• accuracy

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• Precision refers to how good our observations are
  with respect to each other.
• Accuracy refers to how good our results are to
  the true value

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When we talk about precision and accuracy we're
talking about statistics and more specifically
standard deviation.
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Simple Statistics
30.615 30.618 30.614 30.615 30.616 30.614 30.613 3
0.614 30.616 30.618
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The difference between is how we
measure how good our observations are with
respect to each other - precision.If we replace
with the true value we get a measure of
accuracy.Chart1.xls
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Errors in Survey Measurements

• Gross - chart 5.xls
• Systematic - chart 6.xls
• Random

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Errors in derived quantities

• We have measured two distances d1 and d2 in a
  straight line. What is the total distance (D) and
  its standard deviation?
• d1 154.26m and has a SD of 0.01m, d2 175.34m
  and has a SD of 0.05m

D d1 d2 154.26 175.34 329.60m D (d1
e2) (d2 e2) (154.26 .01) (175.34 .05
)
154.27 175.39
329.66 difference 0.06m
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The coordinates of a point A are 311.617m E,
447.245m N. Calculate the coordinates of point B
where qAB 37o 11 20 and sAB 57.916m. What
are the coordinates of B. What effect would
there be of an error in the bearing of 1o and in
the distance of 0.5m.
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Maps and Plans Basic Computations Geometrical
Concepts Errors and Statistics
Background
Distances Angles Height differences
coordinates heights
Measurements
Mid Semester examination
New Technologies
GPS
Practical Surveying
Setting Out
Analysis
Geographical Information Systems
Legalities involved
Cadastral Surveying
Computer assisted surveying